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Thread: I don't know how to solve this problem

  1. #1
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    I don't know how to solve this problem

    \frac{\partial ^2}{\partial x^2}\left(\frac{xy}{2x+y}\right)
    Last edited by topsquark; Mar 14th 2017 at 02:00 AM.
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  2. #2
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    Re: I don't know how to solve this problem

    Quote Originally Posted by jackson990 View Post
    $\frac{\partial ^2}{\partial x^2}\left(\frac{xy}{2x+y}\right)$
    using the quotient rule and treating $y$ as a constant we get

    $\dfrac{\partial}{\partial x}\left(\dfrac{x y}{2x+y}\right) = \dfrac{y(2x+y) - 2xy}{(2x+y)^2} = \left(\dfrac{y}{2x+y}\right)^2$

    $\dfrac{\partial}{\partial x}\left(\dfrac{y}{2x+y}\right)^2 = 2\left(\dfrac{y}{2x+y}\right)\cdot \left(\dfrac{-y}{(2x+y)^2}\right)\cdot 2 = -\dfrac{4y^2}{(2x+y)^3}$

    $\dfrac{\partial^2}{\partial x^2}\left(\dfrac{x y}{2x+y}\right) = -\dfrac{4y^2}{(2x+y)^3}$
    Thanks from jackson990
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